If you live in an area where you rarely drive on packed snow, icy roads, or snow fall greater than 1-2" the OEM all season tires should be OK. However, if you use your i in an area that routinely has heavy snow, snow packed roads, icy conditions, and you must get to where your going no matter what, dedicated winter tires should be considered.
Consumer Reports said it best several years ago; "the best all-season tire will be inferior to the worst dedicated winter tire". Look for a tire that has the Severe Service Symbol on the side (a mountain with a snowflake inside). There are a few all-season tires that have this designation and all winter (snow) tires should have it.
When using winter tires, narrow is best. Don't go wider, 60 to 55 or 65 to 60. You can go to a 165/65-15 for the rear tire as the overall diameter is about the same as the OEM 175/60-15 (less than 1% larger).
Downside of winter tires; high rolling resistance. All that traction comes at the cost of rolling resistance. Expect a noticeable reduction in range. I have only found one brand that makes a low rolling resistance tire with the severe service symbol; Vredestein Quatrac all season tire. Nokian may also have a low rolling resistance severe service symbol tire. For a regular winter tire Dunlop makes the Graspic DS-3 in the OEM sizes.